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Imaginary quadratic fields with class group exponent 5

Abstract:
We show that there are finitely many imaginary quadratic number fields for which the class group has exponent 5. Indeed there are finitely many with exponent at most 6. The proof is based on a method of Pierce [13]. The problem is reduced to one of counting integral points on a certain affine surface. This is tackled using the author's "square-sieve", in conjunction with estimates for exponential sums. The latter are derived using the q-analogue of van der Corput's method. © Walter de Gruyter 2008.
Publication status:
Published

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Publisher copy:
10.1515/FORUM.2008.014

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
FORUM MATHEMATICUM
Volume:
20
Issue:
2
Pages:
275-283
Publication date:
2008-01-01
DOI:
EISSN:
1435-5337
ISSN:
0933-7741
URN:
uuid:29078c90-dae0-4fa6-9d80-8342abb2b340
Source identifiers:
22793
Local pid:
pubs:22793
Language:
English

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